The original attractive force results from a negative Casimir energy. We are
especially interested in conditions that can cause a change in the sign of the
Casimir energy. It can happen, for example, if a mixed boundary condition (BC)
is considered. That is, if Dirichlet or Neumann boundary condition is imposed
on both plates, this force is attractive, but it becomes repulsive when fixing
a plate with the Dirichlet boundary condition and the other plate with Neumann
boundary condition [1]}. In the context of dielectrics
materials, Lifshitz predicted in 1956 that the force is attractive for two
identical dielectric plates in vacuum [2]}. A few years later, in
1961, Lifshitz and colleagues generalized this result by considering a medium
between the dielectrics plates [3]}. As a result, they showed
that, if the two plates and the medium have different dielectric constants,
the force can become repulsive. Experimental verification of the repulsive
Casimir effect was performed at [4]}, by filling the medium with a
dielectric liquid, such that the dielectric constants of the three bodies
involved in the experiment differ causing a repulsive effect. However, if the
two plates have the same dielectric constant, the force is always attractive,
regardless the dielectric constant of the medium [3]}. Indeed,
this last conclusion is a particular result of a non-go theorem [6]},
which states that “the Casimir force between two dielectric
objects, related by reflection, is attractive.” A possible
“loophole” in this theorem may arises when
a chiral material is considered as a medium between the plates
[7]}.
